Numerical confirmation of universality of transmission micro-symmetry relations in a four-probe quantum dot

TL;DR

This paper numerically confirms that certain symmetry relations in a four-probe quantum dot system are universal across different geometries, showing that the Hall resistance behavior is governed by fundamental quantum effects rather than specific structural details.

Contribution

It demonstrates the universality of micro-symmetry relations in quantum dot transport across various shapes and impurity positions, extending previous findings.

Findings

Symmetry relations are preserved despite shape and impurity variations.

Hall resistance behavior is primarily influenced by quantum effects, not geometry.

Universality suggests fundamental underlying principles in quantum transport.

Abstract

We study the crossover behavior of the Hall resistance between the integer quantum Hall regime and a regime dominated by the Aharonov-Bohm oscillations, in a system of 4-probe quantum dot with an artificial impurity confined inside. In a previous study [M. Lei, N.J. Zhu and Hong Guo, Phys. Rev. B. 52, 16784, (1995)], a peculiar set of symmetry relations between various scattering probabilities were found in this crossover regime. In this paper we examine the universality of this set of symmetry relations using different shapes of the quantum dot and positions of the artificial impurity. The symmetry holds for these changes and we conclude that in this transport regime the general behavior of the Hall resistance is determined by the competition of the quantum Hall and Aharonov-Bohm effects, rather than by the detailed shapes of the structure.